An Entanglement-Complexity Generalization of the Geometric Entanglement

TL;DR

This paper introduces a tunable generalization of geometric entanglement using matrix product states, capable of identifying complex entanglement structures and phase transitions in various quantum spin models.

Contribution

It presents a novel, adjustable measure of entanglement complexity that extends geometric entanglement beyond separability, applicable to diverse quantum systems.

Findings

Successfully identifies the AKLT ground state in a toy model

Detects all phases in a Haldane chain with anisotropies

Signals ergodic-localized transition in disordered spin chains

Abstract

We propose a class of generalizations of the geometric entanglement for pure states by exploiting the matrix product state formalism. This generalization is completely divested from the notion of separability and can be freely tuned as a function of the bond dimension to target states which vary in entanglement complexity. We first demonstrate its value in a toy spin-1 model where, unlike the conventional geometric entanglement, it successfully identifies the AKLT ground state. We then investigate the phase diagram of a Haldane chain with uniaxial and rhombic anisotropies, revealing that the generalized geometric entanglement can successfully detect all its phases and their entanglement complexity. Finally we investigate the disordered spin-$1/2$ Heisenberg model, where we find that differences in generalized geometric entanglements can be used as lucrative signatures of the ergodic-localized entanglement transition.